An analytical framework integrating performance characterization and coding theory is proposed to mitigate sneak path (SP) interference in resistive random-access memory (ReRAM) crossbar arrays. The core innovation is identified in the mathematical decomposition of ReRAM’s non-ergodic data-dependent channel into multiple stationary memoryless subchannels. Through information-theoretic analysis, an approximate finite-length characterization of the theoretical lower bound for decoding word error probability (WEP) is established. This is achieved by systematically analyzing the SP occurrence rate in constrained array geometries combined with comprehensive evaluation of both mutual information and dispersion metrics across the decomposed channel components. Building upon this decomposition paradigm, a systematic code construction methodology is developed using density evolution principles for sparse-graph code design. The designed codes not only exhibit capacity-approaching decoding thresholds but also yield word error rate simulation results that are close to the derived WEP bound under practical crossbar configurations.

The sneak path (SP) issue presents a substantial challenge for resistive random-access memory (ReRAM), significantly affecting data storage reliability. The SP rate, which represents the proportion of memory cells impacted by SPs, is a crucial parameter influencing the probability of data detection errors. In this paper, we concentrate on analyzing the probability distribution of the SP rate in ReRAM arrays that incorporate imperfect selectors. Our research indicates that when ReRAM stores data following an independent and identically distributed (i.i.d.) Bernoulli distribution with parameter$q$, and the array size is large, the SP rate approximates a Gaussian distribution. The mean and variance of this distribution can be explicitly derived as functions of the number of selector failures, parameter$q$, and the array size.